SUMMARY We calculated Green's functions of displacements and strains caused by a surface load in surface and subsurface observations. Green's functions of displacements and strains at depth became different from those at the surface for a range of angular distances less than 0.01–0.1°. These Green's functions closely agree with the corresponding Boussinesq approximations for tidal loading at angular distances of less than about 0.01–0.001°. We examined the difference between the ocean tidal loading effect estimated by Green's functions at the surface and the effect for subsurface observations, and found a non-negligible difference when the ratio of distance between the coast and observatory to the deployment depth is smaller than 20. We compared amplitudes and phase shifts of areal and shear strains in the M2 tidal constituent observed by borehole strainmeters at 11 observatories with the theoretical strains using the Green's functions at the deployment depth and those at the surface. The theoretical strains using Green's function at the deployment depth are much closer to the observed strains than theoretical strains at the surface at four observatories where the ratios of distance from the coast to the observatories to the deployment depth are small. These results suggest that Green's functions at the deployment depth are needed to estimate theoretical strains precisely near the coast.

中文翻译：

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精确估计海岸附近海洋潮汐载荷的影响所需的钻孔深度处的格林函数

总结 我们计算了地面和地下观测中由地面载荷引起的位移和应变的格林函数。在小于 0.01-0.1° 的角距离范围内，格林的位移和应变函数在深度处与表面处的函数不同。这些格林函数与角距离小于约 0.01-0.001° 的潮汐载荷的相应 Boussinesq 近似值非常一致。我们检查了格林函数在地表估计的海洋潮汐载荷效应与地下观测效应之间的差异，发现当海岸与观测台之间的距离与部署深度的比值小于 20 时，差异不可忽略。我们将 11 个观测站的钻孔应变仪观测到的 M2 潮汐成分中的面应变和剪切应变的幅度和相移与使用格林函数在部署深度和地表的理论应变进行了比较。在部署深度使用格林函数的理论应变比在四个观测站的表面理论应变更接近观测应变，其中从海岸到观测站的距离与部署深度的比率很小。这些结果表明，部署深度处的格林函数需要精确估计海岸附近的理论应变。在部署深度使用格林函数的理论应变比在四个观测站的表面理论应变更接近观测应变，其中从海岸到观测站的距离与部署深度的比率很小。这些结果表明，部署深度处的格林函数需要精确估计海岸附近的理论应变。在部署深度使用格林函数的理论应变比在四个观测站的表面理论应变更接近观测应变，其中从海岸到观测站的距离与部署深度的比率很小。这些结果表明，部署深度处的格林函数需要精确估计海岸附近的理论应变。